Thinking About Learning

After months and months of trying, it finally happened. A student asked me a question, specifically this question.

“Why do I understand this when you’re here, but when you leave I can’t do it?”

I find that this is often a conundrum that students encounter, especially when they dutifully take notes in class, look at their examples, and then get lost on the homework. When I teach something, or explain something, I am ultimately the one doing the thinking. The students just nod along and memorize what they have seen, and then are unable to duplicate the examples on their own because they have never actually THOUGHT about the process. The best description I have ever found for this is pseudoteaching (MIT physics and hunting monkeys are my favorite), and I believe it should be mandated reading for all teachers.

The problem as I see it, is that so many of our students, and people in general, detest thinking. We like to become familiar with information because when we become familiar with information we are usually able to recognize information, which often will get that hit of dopamine that comes with good grades. Do it enough and it becomes addicting. I frequently run into this behavior from students. It seems like so many of the students in front of me have forgotten nearly everything their previous teachers have taught them. So when I go to teach them, they are insanely driven by quick responses that are externally validated, because they want that satisfaction of being right. When I try to remove the external stimuli of immediate praise and grades, of mind numbing procedural duplication, I am often met with literal withdrawal symptoms. I am not joking about that whatsoever.

I had never really thought of this whole process of teaching an learning until one interaction with one student one day after school. It’s not as though I wasn’t aware of the process involved in mastery of an academic subject, I had just never contemplated what that looks like from a teacher’s perspective. A student came to my room after school to take a test that she had missed earlier and didn’t have a study hall to use. She was struggling. At first came the exasperation that she could remember covering the material, but didn’t remember how to do the problems. We cover information in class, but we seemingly forget so much of what was covered. Rarely do ever think about why that happens.

When students hit that point of struggle, specifically that point when they can acknowledge the familiarity of material, but fail in the execution of material, a dichotomy forms. Frequently students enter denial. We all can recognize the symptoms of denial, I’ve even participated in some of them before. We blame the teacher, saying, “You never covered this.” We sometimes blame our health, saying that I’m too sick. We question the worth of covering subject, asking ourselves, “Why do I have to do this?” We blame our classmates, saying they are too distracting. We might even blame ourselves and say, “I’m just not a math person.” Whatever the reason that is given, denial allows us to avoid confronting the limitations of our own ability and work ethic. Denial allows us to be in a state of mind where we can avoid actually THINKING and ENGAGING with academic material in any sort of significant way. When we then live in a state of denial, we internalize the mechanisms that allow our minds to get through the struggle of school, without learning much of anything, just waiting until we get to the stage where we can quit. (Hello Senioritis, my old friend.)

But back to my story about the girl working on a test after school. She didn’t just live in denial, she hit rock bottom, and in this case it manifested itself as bawling. I’ve had students get teary eyed during tests before, but it is usually tears of frustration and anger, tears that are symptoms of withdrawal. I am so used to students lashing out in frustration (“This is bullshit!”) that I have become almost numb to the symptoms of denial and withdrawal. But that bawling, it lives vividly in my mind because I have witnessed rock bottom so few times, and this was the first. So when she started bawling, I shut the door, pulled up a chair next to her and just talked. I took the test away and shared my own personal story of rock bottom, and we just talked for about an hour and a half. I didn’t know what else to do because hints and instruction at this point would not have been fruitful in any sort of way.

Not much else was accomplished that day, but it did change the nature of the typical student teacher relationship. It instantaneously showed me that no matter what assessment I give, what questions I ask, I will never be able to understand what actually happens inside students’ minds. All the things that I thought represented good student learning, really don’t necessarily mean students are learning anything. They do problems. They ask questions. They listen. But I can’t be sure if they are learning.

It also showed me that displaying your thought process is an incredibly vulnerable thing to do. As long as I stand in front of the room, making math appear easy, my students will almost always feel ashamed when they cannot duplicate the process as easily as me. That’s why my students so desperately want formulas and shortcuts. Because actually displaying their thought process is such a painful experience that most of them can’t handle in front of me out of a fear that they will be humiliated. (That happened when a student left class in tears because she thought I was laughing at her when she was struggling through working a problem.) I could go on and on about how comfort with vulnerability is essential to learning, but that should be something that rests entirely on its own merit. Besides, I tend to ramble enough already.

So, ever since that day of bawling, I have structured my classes to try an elicit rock bottom symptoms from my students. If a student is going to tune me out, fine tune me out. I would rather know a student is blatantly disengaged than be surprised when a student’s superficial engagement ultimately led to failure. It can be a struggle and a drain at times. And some kids don’t need it, but those complacent students living in denial, that have the potential to truly do anything they want, those are the ones that need to hit rock bottom. It finally happened this last Friday.

There was visible frustration as a student realized that she should be able to do this stuff, but couldn’t.

One of my students living in an illusion of superiority finally, finally, slowed down and worked through a problem.

And of course, “Why do I understand this when you’re here, but when you leave I can’t do it?”

It’s a start, but maybe some real education can actually begin.

Is School Really About Education?

Today, and the next few days, I hope to be able to just talk to my students in one of my classes. I plan on using the timing of losing many students to senior class trip, along with having to do a mandated Ohio Means Jobs lesson. Many of the lessons are rather basic, or those that do require a little upper level math feel rather forced, kind of like they were copied straight out of the textbook. Yet somehow it has more career connections because it came from the state website instead of a textbook. But, like usual I need to digress before I start to ramble into something I really didn’t intend to talk about.

I have been using my blog to write about some of the more transformative experiences throughout my education and I spent a good chunk of last night rereading some of them. This wasn’t my first attempt at making a personal website, it just changed from what I originally thought it would be. Originally I was going to make a site to supplement my class, a resource for mathematical information. However, I am a unitasking teacher, so I really didn’t need a website to explain all the different methods I am using. Providing mathematical information was kind of pointless because there are hundreds of websites out there to do that, all of them better than anything I could produce. Why have I stuck with writing this time?

I used to consider myself an educator who happened to use math as my medium. To steal a line from my pastor, my purpose was to, “comfort the afflicted and afflict the comfortable.” My goal was to salvage education for those on the brink, the perennial discipline problems, the helpless, and to push the honor roll students to their limits. I felt like I accomplished this goal during a couple of years, and now I find myself constantly chasing that nostalgic moment.

Several years ago I stumbled across a blog that laid out in rather blunt terms the social contract that exists in most schools. (I didn’t bookmark it at the time and cannot find it again, but I want to make it clear that while I agree with the premise that will follow, I did not originate it.) It laid out a vision of school that really resonated with me after I had a nervous breakdown in front of a couple of students. Authentic learning is an inefficient, messy endeavor that is not conducive to a typical educational setting. A classroom inherently relies on efficiency to educate the masses. The problem is that this education resembles training more than education. To be effectively trained, quiet obedience is necessary, but in-depth thinking and analysis is not. A contract develops between teachers and students in this environment, one where the students agree to be obedient and complacent, and the teachers agree to not really make students think, but rather rely on memorization. Students are willing to sacrifice freedom and opinions in exchange for not being challenged.

School becomes a place where an encyclopedia of examples is memorized, and we denote the ability to memorize with grades.

After I had my nervous breakdown in Calculus I, I started teaching differently. Well, teaching in a traditional sense wouldn’t be the correct description. I talked with my students, explained everything in excruciating detail. Since it was more conversational in nature two things happened. One, it was easier to get off task. Two, the questions in class changed. It was less, “How do you…,” and more, “Why did that happen?” Every so often we would actually lose track of time and class would end with nothing resembling any sort of closure, and simply resume the next day. Instead of intro and hooks, we opened the book, picked a problem and started mathing. As a teacher, I absolutely loved it. Every statement or action I did was directly in response to something the students did, and every statement or action they did was in direct response to something I did.

There was only one problem with this set up. How do I grade an open-ended discussion? What if I abandoned my end of the social contract? No more grades.

It worked better than I could have hoped. No more grades, no more contract, no more complacency, actual thought.

The next year I decided to try it for a full year rather than a quarter with my next Calculus I class. Same result, but with an added bonus. I started to realize that there is a huge difference between productivity and learning. It was after one of our off task conversations, it could have been about college athletics, school rules, or whatever else, but it left me with an odd feeling. By any normal definition of a typical classroom it was a wasted day. But it didn’t feel like that. I felt like something was learned because my students engaged in some level of thinking. Don’t get me wrong, I still knew how to set my foot down and decide we needed to do some math, but I stopped feeling guilty if every second of class wasn’t devoted to math.

Unfortunately the following year I did not have a Calculus I class. Additionally I had a Pre-Calculus class, a topic I hadn’t visited since my sophomore and junior year of high school. I was teaching Pre-Calc in a relatively traditional way, cover previous assignment, introduce topic, go through examples, release students to work independently. One day though, I had assigned the following problem from this book. It’s #18 on page 163.

A car leaves Oak Corners at 11:33 AM traveling south at 70 kmh. At the same time, another car is 65 km west of Oak Corners traveling east at 90 kmh.

a) Express the distance between the cars as a function of the time after the first car left Oak Corners.

b) Show that the cars are closest to each other at noon.

A student in class called me over to help her get started and another student joined in on the conversation. I became momentarily lost in the problem, probably a couple minutes elapsed, but when I looked up to talk to these two students I noticed every other single student had come over to observe. Right there it told me something wasn’t working. My students weren’t making the connections between the concepts I was teaching and the exercises that are supposed to enlighten those concepts. I immediately thought of my previous Calc class where I didn’t separate the concepts from the procedures and quickly sent out this poorly worded email.

I am looking for feedback on how I taught Calc I last year. Bascially, did the method of doing work in a small group and working through problems one at a time help or hinder your prepartation for whatever math, or attitude towards math, that you are encountering outside of high school? I ask because I have been burdened with trying to teach precalculus this year and I feel that my classes are creeping ever closer to the model that I used last year and the year before, just on a larger scale. If you guys feel that it actually helped your preparation I think I will try and do the same group work/pacing that we did with Calc. If it didn’t, I will stick with a more traditional model.

I know the sample size is tiny, but I received rather positive feedback. The closest to negative feedback I received was a student telling me he was on par with his classmates in the honors program where the students came from AP and IB classes. So I tried it with the larger group, and it worked surprisingly well. I had buy in from 12 of 14 students on a regular basis.

From these three years of experience I became comfortable admitting my own shortcomings in front of my students and learning with them at times. I accepted that I will never be able to embrace bell to bell productivity and always call it learning. I realized that the best learning is extremely difficult to pigeon hole into letter grades. Sometimes I would take a day off from math, but it never felt wasted because there is so much more to learn than what can be enlightened by mathematical procedures.

The next year I dropped many of the conventions found in the social contract of school. If the actions we were doing in class didn’t help enlighten mathematical knowledge, then I decided that that action was really about obedience. I stopped homework. I showed movies, played games, or just talked with my freshmen in Algebra I after they had mastered a set amount of material, which served the dual purpose of extrinsic motivation and allowed me to start to build personal connections. I completely eliminated the concept of a grade with my upper level electives and made the classes more about claiming authority over knowledge, rather than going over many different derivative rules.

There are things I can’t control in school, but for the first time I felt like I was actually teaching and the majority of my students were actually learning, instead of the usual dance around the burden of obedience. I had a purpose as an educator.


I no longer feel like I have a purpose as an educator who uses mathematics, but that I am now expected to be a provider of mathematical information, which makes be dependent on obedience. I’ve been told that students are liars (“they will just lie to protect you”). I’ve been told that students are not smart enough to engage with material (“they can’t be expected to push themselves like that”). I’ve been told that students are nothing but disrespectful and rude (“punch them in the face and tell them to shut it”). I could keep going, but I hope the picture is becoming clear. For the past three years, I feel like my work environment has been one that distrusts its most important stakeholders, its students, and places a premium on obedience and complacency.

That’s why I keep writing this time, because I’ve lost the autonomy to have these conversations about obedience with my students. If this was three years ago, I don’t think this blog would exist because it’s contents would exist between me and my students.

Having a Nervous Breakdown

During my second year of teaching Calculus I had a nervous breakdown in front of my students. I can’t remember exactly what topic I was trying to explain, I think it was the idea behind the Fundamental Theorem of Calculus, but I’m not sure. What I do remember was the feeling and how it started.

I was going over some procedure and explaining how to get the correct answer and one of the students asked me a simple question.

“Why did you do that?”

As soon as I thought about it I felt the sinking feeling of not knowing why. I hate that and have talked about it before. This time though, I didn’t respond with a command of just shut up and do the problem, and I did this for a couple of reasons. One, I was going through some graduate school classes that was completely rearranging my concept of knowledge. Two, the class consisted of only two students which had allowed me to develop more of a personal relationship than is typically involved in a classroom.

When I couldn’t explain the mathy stuff to my students beyond a just mimic me response, I stopped teaching. I literally stopped teaching and just sat there in class. After a few minutes I admitted that I had no idea what I was doing. It is blatantly obvious to most people that math that is used in school isn’t like math in reality, so if I can’t even explain what is happening, what’s the point of the entire endeavor?

I imagine that everyone has been in a class where they have thought to themselves, that the teacher has no clue what is going on, but I can’t imagine many people being in a class where the teacher came in on day one and said, “I don’t know what I’m doing…so, let’s get started.” While it wasn’t day one, that was essentially what I was doing in front of my students, admitting that I am clueless.

If I did that in class today I wonder how my students would respond? I fear they would use it as a justification to tune me out more than many of them already do. (He doesn’t know what’s going on why should I bother.) I fear that they would use it as a justification to complain about grades. (How can he give me a C when he doesn’t understand the stuff himself?) But when I admitted my cluelessness to these two Calculus students they didn’t pounce at the opportunity to take control of the class. I was met with empathy and sympathy, and it immediately transformed the class dynamic. No matter how comfortable I had felt with students in the past it was always centered around a me-them type relationship, but from my meltdown to the rest of the year, class took on a more of an us mentality. It was still a classroom, and I still had more mathematical knowledge than them, but I didn’t feel like the dispenser and controller of knowledge anymore. It felt more like I was talking with them rather than talking at them, as if we were exploring together.

What I learned from that moment on was that my classroom needs to be a place where vulnerability is acceptable, though I think I’ve lost that.  We finished out the rest of the year learning Calculus together. Some days were smooth, some days were messy, but it always felt as if it was together. Sometimes we talked about a concept for the entire period with no math written. Some days we worked on procedures from the book. Some days we did other non-math related stuff and embraced the human element of school. Looking back on the experience, it was probably the first time that I felt like authentic learning was occurring in my classroom and was finally finding a vision of what I want education to be.

That moment became the impetus that lead to what I consider the best two years of teaching in my life. Every class seemed to develop some sense of supportive community. I felt free to experiment with ideas and push the limits of my students. Unfortunately I have watched that environment whittle away that past three years. Why don’t I have that accepting, vulnerable, safe, welcoming classroom centered around togetherness? I’m not entirely sure, but I do know much has changed over the past three years. My schedule changed, students have changed, I have changed, administration has changed, technology has changed, testing has changed, all of this leaving me more disillusioned than I have been in a long time. Maybe I have to have one of those coming to Jesus type moments like I did way back in 2011 when I had a nervous breakdown. I don’t know.

All I know for certain is that right now, there are way more days that I leave work unfilled, like my presence at school has served no purpose. I was under no assumption that everyday would be a rewarding bed of roses when I started this profession, but I am tired of feeling like a piece of shit at the end of nearly every day.

Searching for a Purpose

I have been very unhappy with myself lately. While Googling ideas on ways to discuss leadership I came across an entry written by Morgan Guyton.  What he is describing is that vulnerability and leadership can go hand in hand. In a way, leadership can come from the weak and meek. As I read through more of his posts I realized that for the past two years I have been missing the solidarity that I used to have with my students on a regular basis. Every now and then I get a sense that solidarity has come back, but too often it feels like we are separate, like I am living and working in an “us”  and “them” kind of environment.

When I started blogging again I stated that it would be for my own benefit. The whole purpose was to be about reflection. And if OTES doesn’t think that writing about my teaching at 1:27 AM on April 13 doesn’t count as reflection, I don’t know what does.  As I sit here and reflect, I think I lost my sense of purpose. I feel like I have become a teacher I really never wanted to be. I know what I am doing (teaching math), I know how I do that (I use whiteboarding, but there are many different methods), but I feel like I have lost my reason for why. I teach math, the concepts and procedures, but at the end of the day it just feels so empty and shallow.

I feel that as teachers, we continually hear and use rhetoric about the actions we take in school are “in the best interest” of the students. But what always bothered me was that rarely were the students consulted about their “best interest.” It always felt like that “best interest” was just an empty justification thrown around by teachers, administrators, and parents. I am not trying to portray the people behind Common Core, or any other educational fad as self-serving, maniacal, ego-maniacs, but no matter how sincere the belief behind “best interest,” it really isn’t. Our students are unique in so many ways and when they get aggregatized to the extent of most “best interest” initiatives, they lose their uniqueness, leaving many involved on the front lines of education feeling jaded. When our new initiatives don’t work, we then blame the students.

That’s where I am right now.  A couple of years ago I felt much more accomplished as a teacher. It’s not that my methods have drastically changed, they haven’t. Grades and test scores are pretty similar. But now when I go home at the end of the day I don’t feel like I have accomplished anything. Right now I don’t know why I am here. I know I teach math, but why? Right now, I feel like I am an employee at a prison. Right now, I feel like I have otherized my students. Right now, I feel like I have made them a “them.” As long as I am not “them” I am free to blame “them” for the shortcomings of the classroom.

Right now I’ve made my classroom about my methods, my philosophies, and my math. When I started the process of changing my methods and philosophies a couple of years ago, it wasn’t because they were special, but it was because I decided to make a couple of students my priority. This revelation occurred because for the first time I made myself vulnerable to my students. I made myself emotionally vulnerable to my students. I stopped being the arrogant, pompous, self-righteous, sanctimonious, authority teacher I was and confessed that all I really am was a lost asshole of a human being.

When I admitted that to my class, albeit a class of two, I was met with grace, sympathy, and understanding. If the two guys in class had every opportunity to crush my spirit and destroy it, but instead met me with a feeling of solidarity. I slowly began morphing my teaching to improve the learning in my class and over the course of two and a half years. I would be the first to admit that there are aspects of my class that are entirely unconventional. My purpose had shifted from teaching math to being more student focused. I wanted to become the teacher that inspires students to free themselves of the shackles of intellectual servitude that is often experienced in school. I know I can complete this purpose, I have in the past. (Beyond my intuition, I keep a thank you that a student wrote me a couple of years ago. I read it when I need an emotional lift after a rough day.)

I know I can accomplish my goal, but I think that my priorities were misplaced. Changing my methods didn’t change my outcomes, it was changing my mindset. When I made myself vulnerable I felt a solidarity with my students that I think I have lost. I have become an asshole again. My teaching isn’t really about them, it’s about me. I need to reclaim that solidarity because when there is genuine solidarity in a classroom it can be like a sanctuary of grace during a hectic day.

Bad Images of School Spirit

For the past two weeks I have been trying write about how I view the concept of school spirit. It seems like the topic has come up in discussions at staff meetings and even among the students themselves. Every time that I have tried to write I have come up with some kind of imagery that I was going to use an analogy to describe school spirit. At first it was a tripod, then a pyramid. Even a Russian nesting doll came into consideration. Think about that for a second.

The Nesting Doll of School Spirit….ugh, what a waste.

I keep trying to write and I keep second guessing myself because no matter what I use I always feel like I am missing the point. When I feel like I miss the point I feel like I am contributing to the problem rather than solving the problem.

We have brainstormed ideas on activities and many of them sound really neat. I would be excited to try some of them. But I think what we are doing is backwards. The practices that represent a positive school spirit only manifest themselves in the correct environment. And that is where we don’t focus our attention enough. It is the reason that our all of our activities ultimately feel shallow and contrived rather than being authentic. School spirit requires an emotional investment, but we haven’t created an environment where that emotional investment can thrive.

In the post linked above, the author talks about the professional relation between the staff and students. A successful, spirited, supportive school can only exist when there is a collectiveness between the major stakeholders in the school. Students to students, students to staff, staff to staff, it all needs create a cycle that builds a mindset of us. The intrinsic nature of the educational system we live with though, tends to push us apart. We form cliques. Students group themselves by GPAs, extracurriculars, and different career paths. Staff divides themselves into departments, coaches, classified vs. certified, just to name a few. Our schools do not represent an opportunity to unite, but instead drive us apart. When we are driven apart our leaders tend to divide us into groups that suits their own self-interested pursuits and wonder why their followers revolt or resist.

Once we are driven apart we aren’t under any obligation to view our peers, colleagues, students, teachers, and administration as people. We can assign them traits that we would never ascribe to ourselves. We don’t think of them as us, but rather they are something other. We otherize people. As teachers we create assignments, give grades, and demand obedience that we would never wish upon us. As administrators we create rules and climates that are the furthest thing from being warm and inviting. As students we continually tune out teachers, ignore and belittle their effort, and worship credentials rather than knowledge. Our schools have created an environment where we live by the adage, “what have you done for me lately?” If those others won’t give us what we want, well screw them. We hand out detentions and suspensions, give out low grades, assign more homework. We leave to take classes online, take classes at the community college, just flat out skip school. Then we justify our actions by claiming that they deserved it.

We do all of those thing because it provides a barrier that protects us. Until we are willing to be vulnerable in front of each other, we will always have an unsafe environment that will never be supportive, collaborative, learning environment. (On a personal note, I really think that I have been struggling with the vulnerability side the past two years.) When we are vulnerable we place our self-confidence, our self-image in others. When we are vulnerable we inherently trust each other. As a teacher, when I am vulnerable, I am trusting my students to not ridicule me and tear me down. As a student, when I am vulnerable, I am trusting my teachers with my self-esteem. If that trust and vulnerability are mutual we become emotionally invested in each other. Once we are authentically invested in each other, then, and only then, can we begin to build the activities that appear to create a positive school spirit.

Until we learn to give a crap, our culture will be crap.